Logarithmische Konvexität und Ungleichungsscharen (Q1070369)

From the logarithmic convexity of \(t\mapsto (x^ t-1)/t\) (t\(\neq 0\), extended by continuity to \(t=0)\) several inequalities are elegantly deduced, e.g. \[ (1-\frac{1}{n^ 2})(x^ n-1)^ 2<(x^{n-1}- 1)(x^{n+1}-1)<(x^ n-1)^ 2 \] for \(n>1\), \(1\neq x>0\).